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Simplifying x2 + 18x + 71 = 9 Reorder the terms: 71 + 18x + x2 = 9 Solving 71 + 18x + x2 = 9 Solving for variable 'x'. Reorder the terms: 71 + -9 + 18x + x2 = 9 + -9 Combine like terms: 71 + -9 = 62 62 + 18x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 62 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + 18x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + 18x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + 18x + x2 = 0 + -62 18x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 18x + x2 = -62 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -62 + 81 Reorder the terms: 81 + 18x + x2 = -62 + 81 Combine like terms: -62 + 81 = 19 81 + 18x + x2 = 19 Factor a perfect square on the left side: (x + 9)(x + 9) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + 9) equal to 4.358898944 and -4.358898944.Subproblem 1
x + 9 = 4.358898944 Simplifying x + 9 = 4.358898944 Reorder the terms: 9 + x = 4.358898944 Solving 9 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 4.358898944 + -9 Combine like terms: 9 + -9 = 0 0 + x = 4.358898944 + -9 x = 4.358898944 + -9 Combine like terms: 4.358898944 + -9 = -4.641101056 x = -4.641101056 Simplifying x = -4.641101056Subproblem 2
x + 9 = -4.358898944 Simplifying x + 9 = -4.358898944 Reorder the terms: 9 + x = -4.358898944 Solving 9 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -4.358898944 + -9 Combine like terms: 9 + -9 = 0 0 + x = -4.358898944 + -9 x = -4.358898944 + -9 Combine like terms: -4.358898944 + -9 = -13.358898944 x = -13.358898944 Simplifying x = -13.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.641101056, -13.358898944}
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